Aeroalias provided a great answer! Additionally, don't think of a magnetron as a component installed on an aircraft, think of it as a component installed within a black box (in this case, a transmitter, that's part of a system installed on an aircraft).
There are multiple magnetrons listed within the link you provided above. The first part number, 257-0261-020, is the original part number installed within a Collins black box. The next two paragraphs are a cut and paste from the MPD Components, Inc.'s Products website (http://www.mpdcomponents.com/products.htm):
MPD Components, Inc. is a diverse manufacturer capable of providing
total solutions from ceramic insulators to complete RF assemblies. Our
background and expertise is in applied electronics, microwave RF,
Vacuum Electron Devices (VED's) and ceramic-to-metal sealing.
Magnetrons (VED's)--MPD offers positive and negative pulse magnetrons.
Our magnetrons are for pulse applications with the majority being used
for airborne weather radar and beacon magnetrons. Typical peak powers
run from a minimum of 1.3 kW to 10 kW for Honeywell, Sperry, RCA,
Bendix, King, AlliedSignal and Narco radars. Several magnetrons have
You later asked if the transmitter is continuously powered and the technical answer is, "yes...as long as the system is turned on." That might seem like a cop-out answer, but it's true. I "think" you meant to ask, "Does the magnetron continuously transmit?" Without knowing the specific system the magnetron is installed, I don't think anyone can definitively answer how long it transmits, but it wouldn't be continuous or it would overheat. For example, let's say this magnetron is installed in an aircraft radar system--the duty cycle (amount of transmission versus the amount of non-transmission) is going to vary based on what the radar system is designed to display (mode and range). When the system is turned on and placed in a transmitting mode (not "standby"), the system will transmit a pulse, long enough to send the pulse. Then the transmitter will shut down and the receiver circuits will open. This prevents the receiver from taking in a high-powered signal (a received echo is very small). For a pulse radar system, how many times the system transmits is called the "PRF" (Pulse Repetition Frequency or Pulse Recurring Frequency)--measured in pulses per second--and could be hundreds or thousands of times per second (depending again on the purpose of the particular radar system.
One last thing, somebody asked if transponders use magnetrons. I think the answer is "No", but there could be a transponder system that used them. I believe most used a klystron. Regardless of what generates the power of the transmission, what I wanted to say is that a transponder does not transmit the way I described above. For example, an IFF transponder could be set to "normal" mode, operate correctly, and not transmit one time during flight. How? Because a transponder doesn't initiate the process like a radar system. With transponders, an interrogator (airborne or ground system) initiates the process with a "Who are you?" type of signal. "If" the airborne system receives a valid interrogation, the system will transmit a "This is who I am!" type of reply...otherwise, the system will stay in receive mode until it receives a valid interrogation. If an air traffic control radar system or an airborne system believes they're properly interrogating, but there's no reply, they can use a communication system to verbally request the pilot to "identify"...and the pilot flip a switch, forcing the system to electronically transmit. Again, what I described is "normal" IFF operation. In an emergency (fire, hijacking, etc.), a pilot can select an "emergency" mode and the system will automatically start transmitting (squawking) the emergency code.